These hemi-spheroids will necessarily all touch the plane of the parallelogram KI_ik_ at the same instant that O_o_ has reached K_k_.

Which is easy to comprehend, since, of these hemi-spheroids, all those which have their centres along the line CK, touch this plane in the line KI (for this is to be shown in the same way as we have demonstrated the refraction of the oblique ray in the principal section through EF) and all those which have their centres in the line C_c_ will touch the same plane KI in the line I_i_; all these being similar to the hemi-spheroid QM_q_.

Since then the parallelogram K_i_ is that which touches all these spheroids, this same parallelogram will be precisely the continuation of the wave CO_oc_ in the crystal, when O_o_ has arrived at K_k_, because it forms the termination of the movement and because of the quantity of movement which occurs more there than anywhere else: and thus it appears that the piece C of the wave CO_oc_ has its continuation at I; that is to say, that the ray RC is refracted as CI.
From this it is to be noted that the proportion of the refraction for this section of the crystal is that of the line N to the semi-diameter CQ; by which one will easily find the refractions of all incident rays, in the same way as we have shown previously for the case of the section through FE; and the demonstration will be the same.

But it appears that the said proportion of the refraction is less here than in the section through FEB; for it was there the same as the ratio of N to CG, that is to say, as 156,962 to 98,779, very nearly as 8 to 5; and here it is the ratio of N to CQ the major semi-diameter of the spheroid, that is to say, as 156,962 to 105,032, very nearly as 3 to 2, but just a little less.

Which still agrees perfectly with what one finds by observation.
39.